with a twin paradox animation

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by Roger Luebeck


Cite the book, Relativity Trail
Luebeck, R. Relativity Trail. Mpls: L B Writ Publishing, (2008)


Cite this web page
Luebeck, R. (2010, Sept 10). Twin Paradox in Relativity.
https://relativitytrail.com//twin-paradox-relativity.htm


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03/23/2024 note:

The preprint of my journal article is my most comprehensive online document. It includes detailed diagrams and derivations regarding symmetry of measuring between inertial frames.

It is at this link: preprint.special_relativity.pdf
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You won't find literature elsewhere that resembles what you read on this page. This document and the book Relativity Trail stem solely from the author's own contemplations and derivations. Relativity Trail is completetly consistent with, and subsumes, Einstein's treatment.

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A snippet (20 percent) from Twin Paradox in Relativity

Replacing Einstein's postulates:

.. Once again, Einstein's definition of what constitutes a synchronization of two spatially separated clocks of the same inertial frame amounts to a disregard of an analytical incorporation of an absolute frame of reference.

In keeping with this, he utilizes inertial frames to which he arbitrarily assigns the status of "stationary" and "moving". His treatment does not address the question of which clock is actually running slower or faster over any interval of the analysis, nor, identically, the question of which entity's measuring rod is actually shorter. Symmetrical assessments across inertial frames are assumed, without any hope of diagramming the process. Over the course of Einstein's derivation, certain measures must simply be assigned to the entities involved for the sake of satisfying Einstein's postulates of measure.

In the end Einstein concludes, much to his surprise, that there is a time differential between reunited clocks; but with the absolute frame of reference neutralized by his methods, he cannot explain the missing time.

Why is it called a paradox? As we well documented at the beginning of this introduction, Einstein's relativity is almost universally treated as though it precludes any hierarchy of length and clock rates regarding inertial frames. This leads immediately to the state of mind that "there is no truth of the matter" regarding inertial frames. That in turn, creates a seemingly paradoxical situation: Two reunited clocks do show an actual difference in recorded time, as though there must have been a "truth of the matter" regarding their clock rates as they moved uniformly; i.e., a hierarchy of clock rates dependent on a hierarchy of inertial motion.

But Einstein's treatment does not preclude such actual differences of clock rates. In fact, his postulates demand it, as he should have noted at the conclusion of his derivation. By extension of logic, the famous experiments performed around the turn of the century which drove Einstein's postulates also demanded it, if carried to their logical conclusion.

At the conclusion of Einstein's kinematical section, where he noticed the "peculiar" time-keeping differential between reunited clocks, he should have realized that his clock synchronization method was obscuring the reality underlying the symmetrical measures across inertial frames.

Einstein's confusion regarding a universal (absolute) frame of reference versus purely relative frames of reference is plainly evidenced in his 1905 paper on special relativity, "On the Electrodynamics of Moving Bodies", submitted to Annalen der Physik.

In his initial wording, his second postulate states that "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

With the word "definite", Einstein implies that light has an absolute (actual) speed in reality. But he doesn't explicitly state that there is a physically defined universal reference frame against which light has this definite velocity.

Three pages later, when he restates this postulate, he uses a new wording which fundamentally changes the meaning:

"Any ray of light moves in the "stationary system" of coordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body."

Here he replaces "definite" with "determined" and uses quotes around stationary system. With this new wording, he abandons the absolute character of his postulate as initially worded, indicating he is already preparing (with an eye on the results he anticipates) to abandon the very reference frame which could have brought clarity to his treatment.

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That does not mean that Einstein's special relativity is not valuable. Einstein's treatment succeeds in predicting observations of electrodynamical phenomena.

When presenting relativity from the God's eye view, it is obvious that there is no clock paradox. From the God's eye view, light is regarded as having constant speed in an actual sense. (The constancy of measured, i.e. determined, light speed becomes a deduction.)

Thus Einstein's second postulate is so replaced. Or we might say we are restoring Einstein's initial wording of his second postulate.

An actual difference in clock rates follows immediately from this postulate of the absolute nature of light, provided of course, that one assumes that photons are the maker of every relationship (specifically here, the regulators of atomic functioning; but also the carriers of force information and our means for perceiving events).

The consideration of photons being massless particles, along with the consideration that mass and energy are interchangable, serves as the basis for postulating that light has an absolute speed and is also the limiting speed, with the photon having the property of existing in the form of pure energy. The preceding properties of photons and matter were actually known prior to Einstein's theory. Einstein himself, following the lead of Max Planck, introduced the notion of light existing in the form of a quanta of energy.

Einstein's first postulate, which itself pertains only to measures of properties, is the Galilean Principle of Relativity extended to electromagnetism. As seen in the Michelson-Morley experiment, as well as in Galilean mechanical demonstrations, the Principle of Relativity is inextricably bound with synchronization of motion along different axes.

Einstein's first postulate is replaced, in the Gods' eye view, with the notion that there is actual synchronization at the base of our physical structures, for the sake of their stability.

.. end snippet from Twin Paradox in Relativity


Home page:

Relativity Trail, with 192 pages, 65 diagrams and 75 illustrations, will provide you with complete detailed algebraic derivations of all the kinematical effects of special relativity. Everything is charted out in absolute terms against a system at rest with respect to the totality of the universe for perfect clarity as well as soundness of theoretical basis. It is the totality of the universe that imparts the inertial properties of clock rates and lengths which generate the effects of relativity. This is explained in detail in Relativity Trail.


©   2008,  2011,  2022   Roger Luebeck


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